Modern politics is remorseless, and modern politicians cannot opt out. Even when life and limb are at stake, a political leader has always at some point to ask the vulgar question: how will this play?

Although it will not have been the most important thing on her mind in those lurching first minutes on Wednesday afternoon, Theresa May had to ask herself that question about the terror attack on Westminster. While her overriding task was to ensure that the incident was dealt with effectively and safely, she also had to send the right political signals to the terrorists, to parliament and to the public.

An act of terror is an unforeseen moment of high public danger. But it is also a moment of unanticipated political danger for those in power. For political leaders, moments like this are as slippery as a bar of soap in the shower. One terror attack made George W Bush strong, while another confirmed the haplessness of François Hollande. The only firm rule is that terrorist events make a difference.

These are early days. Yet May has had an impressive 48 hours since the shock of the Westminster attack. Her instincts have been sound. She took charge. She was seen to do so. She spoke well on TV on Wednesday night, showing emotion without being illiberal. She commanded the House of Commons in its 90-minute session too, drawing the expected praise from her own party but unexpected statements of respect from Labour and the SNP.

She did this because, in complete contrast to the persona she adopts at prime minister’s questions each week, this time she chose a consensual tone. Above all, she chose the right words. Where Margaret Thatcher would have gone into warrior mode, or Tony Blair into an evangelical one, May talked repeatedly about defending values. The values she invoked ranged from openness, free speech, liberty, human rights and the rule of law to more humdrum virtues like normality and camaraderie. She wrote her own headlines, too: “We are not afraid,” she said, describing PC Keith Palmer as “every inch a hero”.

This consensual approach was the right course. It also allowed her to get some politically difficult information out into the public domain early and without provoking any blowback. May’s statement contained a disturbing admission, one familiar from the 7/7 events and from Woolwich, and which could yet become a stick to beat her with. Khalid Masood had been known to the authorities. He had come to MI5’s attention in the past. But he was off the radar in the run-up to his act of terror. There was no prior intelligence of his readiness to act.

When attacks like this happen people rally round. The popular wisdom is difficult to mistake in London this week. Britain’s wartime self-image as the nation that could take it, that was not afraid, could keep calm and carry on or, this week, go on drinking tea came effortlessly to the fore. Newspapers that are too puffed up with their own importance, especially post-Brexit, got it badly wrong by trying to be divisive or demanding unspecified tough action. A politician who pretended to be Winston Churchill would get it wrong too.

Newspapers that are too puffed up with their own importance got it badly wrong by demanding unspecified tough action

Yet the pressures on prime ministers from terrorism have increased over the years, not stayed the same. Part of this is self-inflicted. Part of it is inflicted by modern media. In the past, terror incidents were primarily a matter for the home secretary not the prime minister. Roy Jenkins, not Wilson, dealt with the Birmingham bombings. When MPs were officially informed about Brighton, it was Leon Brittan who made the statement to the Commons, not Thatcher, even though she had nearly been killed.

But modern politics demands the prime minister’s total engagement. It was Cameron, not his home secretary May, who told the house about the Woolwich events. May is unusual in being a home secretary who has gone on to become prime minister. Modern prime ministers are now not just their own foreign secretaries. They are also their own home secretaries, especially where terrorism is involved. As so often, a significant change in the structure of governance has taken place without fanfare.

Thirty years ago, Amber Rudd would have been the person in charge this week. But May is the inheritor of a form of prime ministership that Blair created. He regarded the terrorist threat as a defining challenge of prime ministerial leadership. May has handled the last 48 hours in a manner that reflects the Blair approach. But she has learned from Blair’s errors too.

The big question for May is whether she really understands the potential of what she said on Wednesday. She has had good 48-hour periods before in her prime ministership. But they have often not been sustained.

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It would be significant if May really thought the values she praised were the values that defined Britain. But it would also be something of a surprise, given her record. If national unity is so important to her, why put the union so much at risk again? If openness to the world matters so much, why insist on breaking with the EU single market? If human rights matter, why flirt so hard with abandoning the European convention on human rights? If the rule of law matters, why stand aside when the judges are trashed by the tabloid press as enemies of the people?

May described London on Wednesday as “the greatest city on Earth”. She is right to be impressed. Yet London’s response to Masood’s mad and bad act on Wednesday is a reminder that the city shares Europe’s values. They have nothing to do with the hard Brexit that May has committed her government to delivering. A Brexit that was consistent with the values that May extolled so well would be a very different from the one she is actually offering.